Locally stabilized space-time finite element methods on anisotropic hexahedral decompositions

Andreas Schafelner

Nov. 24, 2020, 3:30 p.m. ZOOM

We present locally stabilized, conforming space-time finiteelement methods forparabolic evolution equations on hexahedral decompositionsof the space-timecylinder. Tensor-product decompositions allow foranisotropic a priori error es-timates, that are explicit in spatial and temporalmeshsizes. Moreover, tensor-product finite elements are suitable for anisotropicadaptive mesh refinementstrategies provided that an appropriate a posterioridiscretization error estima-tor is available. The large-scale system of space-timefinite element equations isthen solved by means of the Flexible Generalized MinimalResidual (FGMRES)method preconditioned by space-time algebraic multigrid. Wepresent and dis-cuss numerical results for several examples possessingdifferent features.
This work was supported by the Austrian Science Fund (FWF)under grantW1214, project DK4.